Kelly Criterion: Definition, How Formula Works as Risk Management Strategy

Kelly’s Criterion

– Percentage Risk

We discussed the 3 position sizing techniques in the last chapter: 

• Unit per fixed amount
• Percentage Margin
• Percentage Volatility

The combination of position sizing and equity estimation techniques can produce a variety of results, so it is up to you to decide the best combination for your individual needs.

Before delving into the subject, I believe it’s essential to look at another practical position sizing approach known as ‘Percentage Risk’. I’m aware that many traders embrace this method as it is quite straightforward and user-friendly. I would also add that it has even been my go-to practice.

The percentage risk method involves deciding how much ‘loss’ you are willing to accept for a particular trade. This is commonly known as the ‘Stop loss’ – the price at which you decide to close the trade and take any losses. The percentage risk technique can help control the size of the position relative to the risks outlined by your stop loss.

Taking the example of a stock futures, I believe this is an advantageous trade setup to explain how it works.

This intraday chart of Tata Motors from 14th September 2017 at 11:30 AM is displayed with a 15 minute frequency.

I want to discuss why this business transaction is a sensible idea.

Tata Motors is currently at 393.65, making this a price action zone considering it has been tested twice before. That makes the support given by the stock to its intraday price at this level. It can be remembered that when this number was hit both times in the past, the stock decreased from there; therefore there is a chance that it could test 393.65 and go back up to 400 again.

Do take note of the modest dip in price from 400 to 393.65 – I’ve detailed my enthusiasm for trades of this variety in the Technical Analysis module. If you have not yet read it, maybe now is a good time!

Taking into account these considerations, a trader might be encouraged to purchase Tata Motors Futures at 393.65.

What would happen if the trade went the other way? hat is the stop loss?

I observe that there is assistance around 390/-, and I am thus pleased to establish this as a stop loss for the trade.

As you can tell, this is quite an uncomplicated setup.

So the trade would be –

Stock: Tata Motors Limited

Trade: Long

Trade Price: 393.65

Target Price: At least 400

Target value 6.35

Stop loss Price: 390

Stop loss value: 3.65

The reward to risk ratio of 1.7 is remarkable for a single-day investment.

Lot size: 1500

Margin Required: 73.5K

Let’s assume that I have Rs.500,000/- to invest, how many lots of Tata Motors shares can I purchase with the required margin being Rs.73,500/-?

You can purchase up to 6.8 lots, which is the maximum amount.

500000/73500

=6.8

It’s not wise to risk your entire capital on a single trade. If the outcomes doesn’t go as expected, you would be losing Rs.32,850 (3.65 * 1500 * 6). In my opinion, it’s better to spread out your risk.

Ultimately, you would lose-

32850/500000

=6.57% of your capital on one trade.

No matter how successful a trading setup is, it isn’t wise to risk too much capital. Traders usually follow the “Percentage Risk” position sizing trick and don’t exceed risking 1-3% of their total capital for any single trade.

Let’s set a maximum risk level in terms of percentage of total capital; let’s use 1.5%. For this trade, the most I’m willing to accept as a loss is

1.5% * 500000

Rs.7,500/-

I’m only willing to risk a maximum of Rs.7,500/- on any given transaction; anything beyond that is out of bounds for me.

We know the stop loss for this trade is 390 from an entry price of 393.65, the stop loss in absolute Rupee terms is –

393.65 – 390

= 3.65

The loss per lot is –

3.65 * 1500

= 5475

If the stop loss activates, it will cost me Rs.5475 per lot.

To determine the quantity of lots I’m comfortable with risk-wise, I merely have to divide the maximum limit by the amount lost on each trade.

= 7500/5475

= 1.36

I can go ahead and purchase up to 1 lot, resulting in a margin deposit of Rs.73,500/-.

It is sensible to lower the amount of money held back from our total capital and re-examine the maximum loss threshold for this next trade. Let’s revise the maximum loss limit and make a new one.

500000 – 73500

= 426,500

1.5% * 426500

= 6397.5

For the next trade, I will compute the stop loss, multiply that figure with the lot size and divide the maximum risk – 6397.5 – by my loss threshold in order to establish how many lots I can transact.

And so on and so forth!

Do you want to know how the trade went? Well, here’s what happened…

I enjoy trades like these, where the price doesn’t even come close to hitting my stop loss. I had mentioned previously that I was very confident in this one, so now the question is: how do I decide how much to invest when I’m quite sure it will go well? Should I be more daring and put more capital at risk?

Greet Kelly’s Criterion!

– Kelly’s Criterion

John Kelly’s Criterion has an intriguing past. It was initially put forward by Kelly in the 1950s while he was working at Bell Laboratories of AT&T in order to help the telecom company handle long distance telephone noise issues. Surprisingly, it was then taken up by professional gamblers to identify the ideal size of a bet, and soon began to be used for stock market trading. Today, there are numerous traders and investors who utilize Kelly’s Criterion for determining how much to invest. This is likely one of the few tools that both investors and traders use alike.

I’m still puzzled by how I ventured from Telecom to stock markets – despite having a degree in Telecommunications, my knowledge of it is non-existent, yet I have been an active part of Stock markets for more than 13 years! How Kelly’s Criterion managed to cross over between two very different fields is beyond me.

The Kelly’s Criterion helps calculate the optimum stake size, that is, what fraction of our investing resources should be utilized, taking into account a few factors.

We possess data which helps us make a decision about the bet

We possess an advantage when it comes to betting on this particular outcome.

Let’s start with an example of Kelly’s Criterion. This equation produces a percentage, often referred to as the “Kelly’s percent”. The following is what it looks like:

Kelly % = W – [(1-W)/R]

Where,

W = Winning probability

R = Win/Loss ratio.

The likelihood of a win can be determined by dividing the total number of successful trades by the total amount of trades performed.

The win/loss ratio is the average gain of winning trades relative to the average loss of losing trades.

To better comprehend this idea, let’s utilize an instance. Suppose I own a trading system which generated these outcomes regarding Tata Motors, as an example.

Given the above data –

W = Total Number of winners / Total number of trades

= 6/10

=0.6

R = Average Gain / Average Loss

Average gain = Average of [5325, 2312, 4891, 1763, 8675, 4231]

= 4,532

Average loss = Average of [6897, 231, 989, 1980]

=3,274

R = 4532 / 3274

= 1.384

It should be noted that a figure larger than 1 is generally desirable, as it implies that the average gains exceed the average losses.

Let’s input these figures into the Kelly’s Criterion equation –

Kelly % = W – [(1-W)/R]

= 0.6 – [(1-0.6)/1.384]

=0.6 – [0.4/1.384]

= 0.31 or 31%

Kelly’s Criterion tells us that the 11th trade on Tata Motors should have a capital exposure of 31%. This is in accordance with the original school of thought, which outlines that Kelly’s percentage reflects the amount of capital one must use in a trade.

It can be tricky to use the Kelly’s Percentage as it suggests having a capital exposure of 70% for the next trade. Personally I don’t agree with this approach, yet one may wonder why not? After all, a system providing a 70% accuracy rate is quite impressive, thus why not take advantage and increase the bet?

There’s a substantial risk that you could lose as much as 70% of your capital, so proceed with caution.

Given this, let us reconsider the percentage risk position sizing technique we discussed earlier in the chapter.

We employed the percentage risk technique to define exposure for a trade as a fixed factor of capital, such as 1.5%. Modified by Kelly’s criterion, we can choose to alter exposure at our discretion up to 5% – or whatever rate considered suitable.

This means for a given trade, one should not expose more than 5% of their capital. This could be anywhere from 0.1% to the full 5%, and how to decide depends on the individual.

We can use the Kelly percentage for our purpose. For example, if it’s at 30%, then I’d risk 1.5%, and if it’s 70%, that would be 3.5% of the capital on the trade.

A larger Kelly’s percentage means more capital is exposed, and a smaller percentage leads to less exposure.

To better understand Kelly’s Criterion, I recommend watching this video starting at the 10th minute- https://youtu.be/o7YIa1w58Yc